Yeah, it does depend on the shape of the object. Most of the basic theoretical stuff deals with a shockwave forming at the apex of a wedge, so varying the angle of the wedge will change the angle of the shockwave. There's a decent flash based shockwave simulator that NASA put together as part of their idiot's guide to all things aerospace, but I can't find the exact page. This page has a decent explanation of oblique shockwave properties.
Edit: the simulator is about halfway down the page I linked to.
/nerd talk
Right, so I was just wondering if the fact that only the local flow was supersonic (or transitional) makes this theory incorrect like the guy was claiming? I thought it was more a function of shape, rather than freestream velocity. And my god....I cant believe I just typed that. Seriously..../nerd stuff......
